I voted for World of Warcraft due to its undeniable influence, popularity and addictiveness. In fact, it was so influential and popular that I believe that it roped in lots of players who, ordinarily, wouldn't have been interested. You see a lot of unfavorable opinions of WoW nowadays, and much of it seems to come from people who were eventually convinced to get into the game because their friends were hooked on it. I view negative opinions like those less as an indictment of the game and more as a testament to how huge it was. Similarly, I suspect that a lot of players (even those who loved the game) kept playing after they started tiring of it and getting frustrated at it, because of the same peer pressure and/or addictiveness, and tend to remember the reasons why they soured on it more than the reasons why they initially enjoyed it. Because of these reasons, you might find a negative opinion of the game for every positive one nowadays, but I wouldn't call it a "polarizing" game. The original game was anything but polarizing. The criticism has almost entirely been because of the evolution of the player base, the out of control hype and the effects of the expansions (i.e. all things that happened months or years after the game's release).
I played through San Andreas and really enjoyed it, even though I played it almost 10 years after release. I'd say that it was revolutionary for having such a large, open world and had a big hand in making those popular later in the decade. On the other hand, the gameplay and graphics weren't that much different than the two games in the series before it. That didn't really hurt my enjoyment of it, but I think that it makes at least a little difference when judging game of the year. Still, it would probably be my pick if WoW weren't on the list.
I played through Half-Life 2 and enjoyed it, too, but I've never been as high on it as my fellow PC gamers. The original was more groundbreaking and fun to play, IMO. On top of that, the sequel took so long to come out that I was both a bit tired of waiting for it and not as impressed as I could've been if it'd been released years earlier. It pushed the boundaries for graphics and physics at the time, so it was distinctive and influential, but I've just always felt like it gets more praise than it deserves because it was a long-awaited sequel to a great game. If it had been named something other than Half-Life 2, it probably wouldn't be revered like it is.
I tried Halo 2 once and was not impressed. I respect that it was a game changer on consoles and don't blame anyone voting for it, but it was pretty unimpressive to me on PC, where shooters had had equal or better multiplayer, matchmaking and controls for at least 5 years at that point. I appreciate that it made shooters popular on consoles, though, since that led to even more cross-platform shooters. In fact, similar could be said for KOTOR and KOTOR2, which I couldn't get into, but making RPG elements popular on consoles no doubt led to more games with them that I did like (like DA: Origins).